House Rules - Character Creation
Interesting and Flawed Characters
First and foremost; try and make a character that is interesting and not just a bunch of stats optimized to be great in combat. Think about an interesting background, and I'm not talking about the backgrounds that you select from the book, although you can use the traits/flaw/ideal/bonds tables there as inspiration. You should have a good idea of what your character did in the past and how it got here. How was their childhood, what did their parents do? Give it some family members and friends/enemies for flavor and potential plot hooks. No Chaotic Neutral murder-hobos with no living family or friends.
Flaws make for interesting characters; try and distribute your ability scores in more interesting ways, pick some (less useful) skills that reflect your career before you became an adventurer, etc. Also worth thinking about is certain phobias (spiders, tight spaces, etc.), character flaws (overbearing, afraid of commitment, etc.), and other things that make your character more rounded without making them unplayable.
Rulebooks Used
To keep things simple we only use races/classes/spells/etc. from the 2014 PHB and no other books, with a few exceptions below.
Ability Scores
Characters get the standard ability score array; 15, 14, 13, 12, 10, 8.
We use the racial Ability Score Increase from the 2014 PHB and the Variant Human Traits (page 31); humans get +1 to two ability scores, proficiency in one skill of your choice, one feat of your choice.
Races/Classes
Dragonborn, Drow, Tieflings, and Sorcerers are not available due to story reasons, but if you really, really want to, talk to the DM.
Backgrounds
Backgrounds from any of the official books can be used. I also found a list of 1200 trinkets, most of which are great.
Languages
Next to the ones in the PHB, there's also Dark Speech (used by followers of evil gods, etc.) and Ancient (precursor to Common).
Skills
Players get to choose one extra skill proficiency more than normal and there are a number of new skills, see House Rules - Skills.
Feats
Some feats have been changed and a number of feats from other books are allowed, see House Rules - Feats.
Custom Character Stuff
If you have a very specific character idea I might be willing to make a small change in a race/class ability, etc. if we can work this out together. But it won't be something that will make your character more powerful than before, more likely the opposite. See examples here.
DM Fiat
The DM will always need to give his fiat to any character concept, even if it is strictly within the rules it could still be unsuitable for the campaign.
For a new campaign
A fun way to start a campaign in a city; the players write rumors about their characters (true, mostly true, false) and then distribute rumors to others.